The bear, sitting in the back of the car, appeared to play a vuvuzuela, a plastic horn that became popular with soccer fans during the South African World Cup.
In the video, the bear is seen sitting next to a trainer. It raised its arms in a cheer before appearing get a treat.
The same bear was filmed riding in the sidecar of a motorcycle in Russia in September last year.
Other YouTube videos that appear to feature the bear show it playing a trumpet, dancing and hula hooping. Those videos date back to at least 2013.
"Bears used in performances are carted around in cramped cages, and trainers typically whip, beat, and otherwise torment them to teach them to obey out of fear," PETA stated in its letter to Moscow. "It's also dangerous to take these animals onto a public street: Bears can run up to 40 miles per hour, faster than any human. Those who have been denied everything that's natural and important to them have also been known to lash out in frustration by biting, mauling, or otherwise attacking handlers and members of the public."